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1e4...White starts with a logical pawn move. Remember: On their first move (when a pawn is on its initial square), pawns have the option to go one or two squares forward. On all other moves a pawn can only go one square straight forward.1...e5Black replies with a pawn move himself. Why does Black play this move?

One of the key ideas of this opening is to quickly control the center . This is achieved by placing a pawn in the center on the first move (1...e5), a move which also liberates the Black’s dark-squared bishop and queen.
2Nf3...A good move!
Remember: A knight moves in an L-shape over the squares. This means that this chess piece at first goes two squares to the left, to the right, back- or forwards and then one square into horizontal or vertical direction. Of course, it is also possible to move in the same shape in reverse – the knight can also move one square into any direction in the beginning and then across or down two squares.
By playing 2.Nf3, White immediately attacks the Black central pawn on e5. Afterwards, White moves his bishop to the dangerous c4 square (3.Bc4) from where it eyes Black’s potentially weak f7 pawn. Moreover, by bringing the bishop into play, White prepares to castle on the next move.
2...Nc6Black moves his knight, too. Thereby, he protects the pawn on e5.3Bc4...White brings his bishop into play.
Remember:
The bishop is the ruler over the diagonals of the chess board. While there is no piece in their way, bishops can move in any direction diagonally, as many squares as desired. They can capture any piece which is within their reach.
3...Bc54O-O...Finally, White brings his king to safety.

Remember: The king can participate in a special move called “castling”. When you castle, you simultaneously move your king and one of your rooks. Thereby, you move the king two squares towards your rook and then move the rook to the square over which the king crossed.
4...Nf6Black brings his knight into the game.5d3...White moves his pawn one square forward.5...O-OBlack castles on the kingside.6Qe2...White moves his queen.6...d6Black moves his d-pawn.7c3...White moves another pawn.7...Re8Black moves his rook.8Rd1...White moves his rook.